a rectangular box has dimensions 9cm by 6 cm by 24 cm. a second rectangular box has volume one-half of the first and has a base 6 cm by 4 cm.what is the height of the second box

1st Box

V = Lwh
V = 9 * 6 * 24
V = 1296

2nd box
V = 1/2 (1296) = 648
V = Lwh
648 = 6(4)h

Solve for h

To find the height of the second box, we can use the formula for the volume of a rectangular box:

Volume = Length x Width x Height

Let's start by calculating the volume of the first box:

Volume1 = 9 cm x 6 cm x 24 cm
Volume1 = 1296 cm^3

The volume of the second box is given as one-half of the first box. So we can set up the equation:

Volume2 = (1/2) x Volume1

To find the height of the second box, we need to rearrange the formula for volume as follows:

Height2 = Volume2 / (Length2 x Width2)

Given that the base of the second box is 6 cm by 4 cm, we substitute the values:

Height2 = (1/2) x Volume1 / (6 cm x 4 cm)
Height2 = (1/2) x 1296 cm^3 / (6 cm x 4 cm)
Height2 = 648 cm^3 / 24 cm^2
Height2 = 27 cm

Therefore, the height of the second box is 27 cm.

To find the height of the second box, we need to calculate its volume first.

The volume of a rectangular box is given by the formula: volume = length × width × height.

Given that the dimensions of the second box are 6 cm by 4 cm for the base, we can substitute these values into the formula.

Volume of the second box = length × width × height
Volume of the second box = 6 cm × 4 cm × height

Now, we know that the volume of the second box is one-half of the volume of the first box. The volume of the first box can be calculated using its given dimensions of 9 cm by 6 cm by 24 cm.

Volume of the first box = 9 cm × 6 cm × 24 cm

Since the volume of the second box is half of the first box, we can equate the two volumes:

Volume of the second box = 1/2 × Volume of the first box

6 cm × 4 cm × height = 1/2 × (9 cm × 6 cm × 24 cm)

Now, we can solve for the height of the second box:

6 cm × 4 cm × height = 1/2 × (9 cm × 6 cm × 24 cm)

Divide both sides by (6 cm × 4 cm):

height = 1/2 × (9 cm × 6 cm × 24 cm) / (6 cm × 4 cm)

height = (9 cm × 24 cm) / (2 × 6 cm)

height = (9 cm × 24 cm) / 12 cm

height = 9 cm × 2 cm

height = 18 cm

Therefore, the height of the second box is 18 cm.